This article focuses on physics-informed machine learning (PIML), a sub-domain of machine learning that combines physical knowledge and empirical data to enhance performance in tasks involving a physical mechanism. The authors propose a general regression problem where the empirical risk is regularized by a partial differential equation. They demonstrate that for linear differential priors, the problem can be formulated as a kernel regression task. The authors also discuss the concept of hybrid modeling and explore its benefits in empirical risk minimization.
Publication date: 12 Feb 2024
Project Page: arXiv:2402.07514v1
Paper: https://arxiv.org/pdf/2402.07514
